Problem: Simplify the expression. $(6y^{4}+4y^{3}+7y^{2})(y^{3}+2y^{2})$
Explanation: First use the distributive property. $ 6 y^4 ( y^3) + 6 y^4 (2 y^2) + 4 y^3 ( y^3) + 4 y^3 (2 y^2) + 7 y^2 ( y^3) + 7 y^2 (2 y^2) $ Simplify. $ 6y^{7} + 12y^{6} + 4y^{6} + 8y^{5} + 7y^{5} + 14y^{4} $ $6y^{7}+16y^{6}+15y^{5}+14y^{4}$ Identify like terms. $ { 6y^{7}} \color{#DF0030} {+ 12y^{6}} \color{#DF0030} {+ 4y^{6}} {+ 8y^{5}} {+ 7y^{5}} {+ 14y^{4}} $ Add the coefficients. $ { 6y^{7}} \color{#DF0030} {+ 16y^{6}} {+ 15y^{5}} {+ 14y^{4}} $